Moduli of relative stable maps to P^1: cut-and-paste invariants

 I will give an introduction to the moduli space of genus zero rubber stable maps to P^1, relative to 0 and infinity, with fixed ramification profiles. Then I will discuss two recent results on the topology of these moduli spaces. The first concerns a chamber structure for the classes of these moduli spaces in the Grothendieck ring of varieties. The second gives a recursive algorithm for the calculation of the Euler characteristic, in the case where the maps are fully ramified over zero, and unramified over infinity. If time permits, I will also discuss some potential future directions.

The synchronous discussion for Siddarth Kannan’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2022-04-01-sk (and will be deleted after ~3-7 days).